Consistently Constrained SL(N) WZWN Models and Classical Exchange Algebra

Currents of the SL(N) WZWN model are constrained so that the remaining symmetry is a symmetry of constrained currents as well. Such consistency enables us to study the Poisson structure of constrained SL(N) WZWN models properly. We establish the Poisson brackets which satisfy the Jacobi identities owing to the classical Yang-Baxter equation. The Virasoro algebra is shown by using them. An SL(N) conformal primary is constructed. It satisfies a quadratic algebra, which might become an exchange algebra by its quantum deformation.